The invention relates to a method for making a flanged length of pipe having a lining of plastic material. It is known, particularly in the chemical industry, to make piping formed of steel tubes having a lining of plastic material, particularly of fluorinated resin such as PTFE. These tubes have very good resistance to corrosion from chemical products in a wide range of temperatures. Depending on its nature, the lining does not adhere or adheres very weakly to the metal tube. The resistance to leakage of piping made of tubes of the known type is thus threatened, particularly at junctions between two tubes connected by end flanges. Any creep or shrinkage of the plastic lining material at the flanges can compromise the resistance of the joint to leakage.